YOU would have to apply for the TRV - not her.
However given your refugee status, the TRV is guaranteed to be refused. I don't see the point in applying. To be approved, you need to show that you have strong ties to your home country and have no plans on remaining in Canada long term. Since you are a refugee, you can't show ties to your home country and it's quite clear you're trying to settle somewhere else. Applying for a TRV will be a waste of money.
